Networks of polarized evolutionary processors
Information Sciences: an International Journal
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This work is a continuation of the research started in [2] and [6] where one has considered a mechanism inspired from cell biology, namely networks of evolutionary processors, that is networks whose nodes are very simple processors able to perform just one type of point mutation (insertion, deletion or substitution of a symbol). These nodes are endowed with filters which are defined by some membership or random context condition. Each processor placed in a node is a very simple processor, an evolutionary processor. By an evolutionary processor we mean a processor which is able to perform very simple operations, namely point mutations in a DNA sequence (insertion, deletion or substitution of a pair of nucleotides). More generally, each node may be viewed as a cell having a genetic information encoded in DNA sequences which may evolve by local evolutionary events, that is point mutations. Each node is specialized just for one of these evolutionary operations. Furthermore, the data in each node is organized in the form of multisets of strings, each copy being processed in parallel such that all the possible evolutions events that can take place do actually take place. These networks may be used as language (macroset) generating devices or as computational ones. Here, we consider them as computational mechanisms and show how an NP-complete problem can be solved in linear time. It is worth mentioning here the similarity of this model to that of a P system, a new computing model inspired by the hierarchical and modularized cell structure recently proposed in [4, 5]. Networks of evolutionary processors (NEP) [2, 6] are language generating device, if we look at the strings collected in the output node. We can also look at them as doing some computation. If we consider these networks with nodes having filters defined by random context conditions, which seems to be closer to the recent possibilities of biological implementation, then using these simple mechanisms we can solve NP-complete problems in linear time. Such solutions are presented for the Bounded Post Correspondence Problem in [1], for the 3-Colorability Problem in [2] and for the Common Algorithmic Problem in [3]. As a further step, in [3] the so-called hybrid networks of evolutionary processors are considered. Here deletion node or insertion node has its own working mode (performs the operation at any position, in the left-hand end or in the right-hand end of the word) and different nodes are allowed to use different ways of filtering. Thus, the same network may have nodes where the deletion operation can be performed at arbitrary position and nodes where the deletion can be done only at right-end of the word. This research is focused on the similarities of Neural Networks and Networks of Evolutionary Processors in oder to include a learning stage in NEPs able to solve different problems with the same architecture. First step, we simplify NEPs by moving the filters from the nodes to the edges. Each edge is viewed as a two-way channel such that input and output filters coincide. NEPs and NEP with filtered connections can be consired universal models since the are able to solve NP-problems. The great disadvantage is that a given NEP/NEPFC can olny solve a given problem, if it is necessary to solve another problem (maybe a little variation) then another diferent NEP/NEPFC has to be implemented. The idea of learning tries to undertake such disadvantage proposing a model able to solve diferent kinds of problems (that is a general class of problems). This research shows the evolution of natural computation models, starting from Artificial Neural Networks and going to Networks of Evolutionary Processors. NEPs model has been modified in order to simplify the proccess activity. There are other learning schemas that can be studied, for example: the addition of rules to the connections instead of using a distance measure. There are a lof of open problems that need to be solved in order to show the computational power of this model, but the possibility to compute NP-problems is promising apart from the massive parallelization and non-determinism of the model.